Download The Effect of Text Length in Crowdsourced Multiple Choice Questions

Crowdsourcing Breakthroughs for Language Technology Applications
AAAI Technical Report WS-15-24
The Effect of Text Length in Crowdsourced Multiple Choice Questions
Sarah K. K. Luger
Institute for Language, Cognition and Computation
The University of Edinburgh
Edinburgh, UK
[email protected]
ideal data is very difficult, if not impossible, to obtain. The
use of crowdsourced, human-annotated, or “human-in-theloop” data has emerged as an important resource for human judgments including answering exam questions. For
example, Amazon’s Mechanical Turk (Amazon 2013) and
the crowdsourcing company Crowdflower (Biewald and
Van Pelt 2013) both provide avenues to gather human
judgments on myriad tasks (Callison-Burch 2009). As described in greater detail in the Data Section, PeerWise was
chosen for this work because it had extensive metadata on
the questions and answers, and also because it is open
source software.
Abstract
Automated systems that aid in the development of Multiple
Choice Questions (MCQs) have value for both educators,
who spend large amounts of time creating novel questions,
and students, who spend a great deal of effort both practicing for and taking tests. The current approach for measuring
question difficulty in MCQs relies on models of how good
pupils will perform and contrasts that with their lowerperforming peers. MCQs can be difficult in many ways.
This paper looks specifically at the effect of both the number of words in the question stem and in the answer options
on question difficulty. This work is based on the hypothesis
that questions are more difficult if the stem of the question
and the answer options are semantically far apart. This hypothesis can be normalized, in part, with an analysis of the
length of texts being compared. The MCQs used in the experiments were voluntarily authored by university students
in biology courses. Future work includes additional experiments utilizing other aspects of this extensive crowdsourced
data set.
Multiple Choice Questions
To measure the usefulness of exam questions, researchers
have devised methods for judging both the difficulty of the
question and the differentiation power of the answer options (Patz and Junker 1999) and (Beguin and Glas 2001).
One such approach is Item Analysis Theory (Gronlund
1981). The analysis of questions based on how students
perform in a group with the goal of improving exam-based
MCQs is broadly called Test Item Difficulty. Within the
study of Test Item Difficulty are several measures including Item Analysis, which evaluate how each student performed based on which answer choice he or she made.
Comprehension and aptitude tests seek to present questions that can be correctly answered by students who understand the subject matter and to confuse all other students with seemingly viable alternate answer options (distractors). A good or difficult distractor is one that catches
or distracts more bad students than good students.
A high-scoring student is one who answers most questions correctly, but when their answers are incorrect,
chooses the best distractors. A low-scoring student will
choose any of the answer options seemingly at random. A
difficult question is one whose answer options are all
deemed viable to a high-scoring student. With a difficult
Introduction
Crowdsourcing presents an alternate method from academic, institutional, and research-oriented document annotations for gathering useful, human judgment data. Measuring the quality of the participating workers’ ouput and the
difficulty of the individual tasks can be complex. Effective
measurement is integral in defining worker payment and
designing the annotation tasks that are often structured as
pipelines of gated tasks or as decision trees. In the case of
the experiments presented in this paper, MCQs will be
assessed for difficulty and the amount of text in the questions and answer options will be analyzed.
The use of standardized comprehension or aptitude exams requires having access to sets of exam data, which
include the questions and detailed, question-by-question
results from thousands of students. Unfortunately, such
Copyright © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
16
question, the high-scoring cohort will behave like lowscoring students, with a near equal spread of multiple distractors being chosen.
A MCQ or item consists of several parts. The stem, or
question statement, presents a query that is best answered
by one answer option. The answer options, or answer alternates, include both the answer and distractors. In the
following example, the item is the question statement
(“Which hormone secretion pattern is directly affected
from jet lag”) and the four answer options (A-D). This
question, from the student-authored question bank called
PeerWise (Denny 2009). This question was answered 282
times and 192 students chose the correct answer A.
as shared edges as noted in Table 1. Thus, the data contains
an incomplete, or sparse exam, as seen in Table 1.
Course
Total number of students
Total number of questions
Shared edges between the
questions and students
2
887
132
31314
Table 1: Data characteristics from the two academic courses. A
shared edge represents a question answered by a student.
One potential research problem is the hypothesis that
PeerWise attracts the better-performing students to practice
and build their expertise in a field. The better students may
tend to both author and answer more questions than their
lower-performing peers. Thus, the PeerWise system may
skew Item Analysis from a more conventional normal distribution across performance cohorts to a tight cluster of
top-scoring students versus a long tail of the middle- and
lowest-performing students. This hypothesis was tested
and revealed that a sufficiently large group of potential
students participated in the exam for meaningful Item
Analysis (Luger and Bowles 2013). Consequently, the bell
curve composed of the three performance cohorts–lowest,
middle, and highest-scoring students–did shift to the left,
but the three cohorts were distinctly discriminated.
The PeerWise data has an exhaustive amount of detailed
information that covers the authoring and taking of courserelated questions. Much of this information is outside the
scope of analyzing question difficulty. There is sufficient
additional question information for myriad research projects, but there are a few characteristics of the data in general that reflect its value for this and additional research.
These characteristics are as follows:
Example 1: Which hormone secretion pattern is directly
affected from jet lag?
A. Cortisol (correct answer)
B. Insulin
1
1055
148
31019
C. Thyroid Hormone
D. Adrenaline
A question may be difficult in many ways. The stem
may be confusing or poorly scoped. The topic of the stem
may be from an obscure corner of a discipline or use ambiguous terminology. Further, when a question has multiple answer options, high-quality incorrect options and discriminating distractors can make a question difficult. The
experiments in this paper are based on questions being
difficult because the words used in the question stem are
not similar to the words used in the answer options.
Using Crowdsourced Data
I procured data for two sets of MCQs from university-level
introductory biology classes using the PeerWise question
creation system. PeerWise consists of questions that are
created by students and answered by their classmates. Instructors can review the questions or use some of the better
questions for future exams. Since answering these questions may not be compulsory, the resulting data is a set of
questions that have been answered by students but not all
of the questions have been answered by the same students.
The process of choosing questions for the experiments
consisted of automatically collecting the subset of questions that used inverse definition constructions such as "is
called," "known as," and "is named". Inverse definition
questions describe a term or process by providing a definition and seek the name of the process. This question format
is frequently used in the sciences where mastering domainspecific concepts are a key measure of comprehension.
An exam is a set of students who have answered the
same questions. The PeerWise data sets consist of students
who have answered some questions, but not necessarily the
same questions from a set. In a graph, these may be viewed
•
•
•
•
•
•
•
•
17
The fewest number of questions answered by any
of the students was 1. 101 students in course 1 answered only 1 question; 152 students in course 2
answered only 1 question.
112 was the most questions answered by a student
in course 1; 11 students answered 112.
The average number of questions answered in
course 1 was 26.6 and in course 2 was 35.8.
No student answered a question more than once.
None of the questions were so easy that all of the
students answered them correctly, nor so hard that
none of them got them correct.
The most times a single question was answered in
course 1 was 439; the least was 89.
In course 2, 331 was the maximum number of
times a question was answered, 132 the minimum.
There were 62,333 distinct answers or questions
that were answered in total.
•
•
There were 20,532 incorrect answers of the total
62,333 answers, or 32.7%.
There were 14,094 question ratings; each of the
sets’ 280 total questions were rated at least once.
questions best controlled for stem word bag size and what
method best controlled for answer option length? The concern was a larger stem bag size might support more correct
answers.
The “Define: X” experiment used an API to automatically return the top 50 definitions for each answer option.
Then, the text of the original question stem was compared
to each definition’s text using Lucene (Apache 2013), incorporating both bag-of-words and WordNet weights
(Princeton University 2010). The answer option producing
the individual definition with the most text overlap was
deemed correct.
The subsequent query type experiment used sampling
methods, where the sample size was justified according to
appropriate statistical criteria (Feller 1950). Random sampling selected questions representing the three stem size
bags present in the question set. There were questions with
5 and fewer content words, 6 to 9 content words, and 10 or
more content words.
As Table 2 shows, questions with 6 or more words in the
stem were answered correctly more often than those with
shorter stems. This suggests that the greater the amount of
information provided in the query, the more likely the
chance of getting the answer correct in the experiments
performed. In the “Define: X” experiment, the search engine shortcut “Define: X" is utilized where "X" is the term
being defined. In this experiment, each of the answer options is automatically sent to a search engine using this
“Define: X” pattern and the results of the query are compared to the text of the question.
Close analysis of the question answer options for concept identification showed three answer types: 1 word, 2
words (usually a colocation), and more than 2 words. I
randomly selected questions based on these answer alternatives and tested how the “Define: X” query performed on
these classes of answers. The results are in Table 3.
Analysis of the student exam results suggests a method
for classifying the output of the automated system that parallels the human results. This supports my underlying belief that the closeness of answer options to the question
stem and to one other as well is reflected in student results.
When a student is choosing an answer to an inverse definition question, he or she is in some manner choosing the
closest concept, process, or term that sufficiently fulfills
the description given in the question stem. Based on this
perception, a difficult question is one where the answer
options are not only closely related terms but also meaningfully linked to the question stem. In other words, my
research compared how students selected answer options
with how the automated system found shared terms in the
definitions of the answer options and the original question
stem.
Mitkov et al. introduces distractor classes, which are a
way of grouping how well an answer option "distracted"
low-performing students as opposed to their higher- performing peers (Mitkov et al. 2006). The four distractor
classes are "good" or useful distractors, "poor" distractors,
not useful distractors, and distractors that confer no discriminating power.
Good distractors are negative numbers indicating that
they attracted more low-scoring students than high-scoring
ones. Poor distractors are positive numbers because they
are chosen by more high-performing students than lowperforming ones. The goal of exams is to differentiate performance groups of students and distract less-prepared
students.
My hypothesis for generating a model of question difficulty is focused on how many distractors with negative
(good) values there are for a given question. One way that
MCQs can be hard is when there are several strong answer
options. When multiple answer options have positive numbers, there are answer options with strong distraction power. As noted earlier, in this case, good students act like
their lower-performing peers conventionally do and spread
their answer choice among several answer options. Difficulty can be measured by the total number of students who
answered a question correctly divided by the number of
students who took the exam. Difficulty can also be measured by how many good distractors are in a question.
Query type
Total percent correct
Correct with stems of 10 words
and greater
Correct with stems of 6-9 words
“Define: X”
57%
100%
40%
Correct with stems of 5 and fewer
33%
Table 2: Results controlling for stem length from the
“Define: X” experiment.
The nature of inverse definition questions is to present a
definition and seek the concept being defined. In the biology domain, the answer options are concepts and they are
primarily 1 word terms or 2 word noun phrases that colocate or are paired to indicate one concept. In the experiments, the web query with the most word overlap with the
question stem was used as the "choice" of the system.
Methodology and Results
There are two questions that arose from the early data
analysis: What method for answering inverse definition
18
Future Work
Answer option
length
1 word
2 words
>2 words
Query type
“Define: X”
83%
50%
100%
The next steps in this research focus on comparing these
results to those from MCQs generated by professional educators. In addition, more sophisticated natural language
processing techniques could be introduced to extend the
text comparisons. For example, it would be interesting to
observe both how the “Define: X” pattern worked on different types of distractor classes and the role that text
length played in those results. Finally, there is additional
information on the students and questions that could lead
to deeper analysis of the dataset.
Table 3: Results controlling for answer option length from the
“Define: X” experiment.
Table 3 shows that the “Define: X” query type performed best with varied answer option length. Perhaps, this
is related to the underlying query methodology that uses
the "Define: X" shortcut to search specifically for definitions. Thus, multi-word definitions are maintained as colocated words when they are sent to the web for results. Concepts such as "active transport" are defined as a unit and
not individually with the definition of "active" and
"transport" combined. The returned definitions were compared to the question stem and this approach does moderately well when stem length is controlled.
References
Amazon.
2013.
Amazon’s
mechanical
turk.
http://www.mturk.com/.
Apache. 2013. Lucene. http://lucene.apache.org/.
Beguin, A. A., and Glas, C. 2001. Mcmc estimation and some
model-fit analysis of multidimensional irt models. In Psychometrika, Vol. 66, No. 4, pp. 541-562.
Biewald, L., and Van Pelt, C. 2013. Crowdflower.
http://www.crowdflower.com/.
Callison-Burch, C. 2009. Fast, cheap, and creative: evaluating
translation quality using amazons mechanical turk. In EMNLP
09: Proceedings of the 2009 Conference on Empirical Methods in
Natural Language Processing.
Denny, P. 2009. Peerwise. http://peerwise.cs.auckland.ac.nz/.
Feller, W. 1950. An Introduction to Probability Theory and Its
Applications. John Wiley and Sons, Inc.
Gronlund, N. E. 1981. Measurement and Evaluation in Teaching.
Macmillan, 4 edition.
Luger, S. 2011. A graph theory approach for generating multiple
choice exams. In 2011 AAAI Fall Symposium on Question Generation.
Luger, S. and Bowles, J. 2013. An analysis of question quality
and user performance in crowdsourced exams. In Proceedings of
the 2013 Workshop on Data-Driven User Behavioral Modelling
and Mining from Social Media at CIKM 2013. pp. 29-32.
Mitkov, R., Ha, L. A., and Karamanis, N. 2006. A computeraided environment for generating multiple choice test items. In
Natural Language Engineering 12(2) pp. 177-194.
Patz, R. J., and Junker, B. W. 1999. Applications and extensions
of mcmc in irt: Multiple item types, missing data, and rated responses. In Journal of Educational and Behavioral Statistics, Vol.
24, No. 4 (Winter, 1999), pp. 342-366.
Princeton
University.
2010.
About
WordNet.
http://www.wordnet.princeton.edu/.
Raykar, V.C.; Yu, S.; Zhao, L.H.; Valadez, G.H.; Florin, C.; Bogoni, L.; Moy, L. 2010. Learning from crowds. Journal of Machine Learning Research Vol. 11 pp. 1297-1322.
Whitehall, J.; Ruvolo, P.; Wu, T.; Bergsma, J., and Movellan, J.
2009. Whose vote should count more: optimal integration of labels from labelers of unknown expertise. Advances in Neural
Information Processing Systems.
Example 2: What type of glia cells engulfs and destroys
micro-organisms and debris?
A. Astrocytes
B. Microglia (correct answer)
C. Ependymal Cells
D. Oligodendrocytes
E. Schwann Cells
Some of these data analysis issues are exemplified by
Example 2. The two highest scoring "Define: X" results in
Example 2 supported "Ependymal Cells" and "Schwann
Cells." Neither result is the correct answer but each shares
the term "cells" with the question stem. "Glia" is the more
important word in the noun phrase "glia cells" and it appears as the root of the correct answer "Microglia." Unfortunately, this match was not caught because "microglia"
was not separated into its constituent parts and there was
no weighting of the word component matches that would
have supported a different, correct result.
The biology domain uses specific scientific terminology
that often adheres to Latin and Greek-based word templates. "Micro" is a prefix that could be used with other
similar biology prefixes to identify or decompose words
for possible matching. Domain-specific spelling variants
should also be incorporated. "Micro-organism," which appears as it was written by a student, could match "micro,"
"organism," "micro-organism," "micro organism," but most
importantly, it should first match "microorganism" because
that is the correct spelling of the word in full. Similarly, the
suffixes "-cytes" and "-cyto" mean "cells." Incorporating a
table of biological terms and their variants would increase
successful matching. In addition, this example shows a
limit on the “Define: X” component of the experiment
pipeline and area for future system improvements.
19